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Integrable systems, symmetries and representations

Evidence pointing towards a supersymmetric extension of the standard model of particle physics has rendered the deeper understanding of supersymmetric gauge theory a priority. EU-funded scientists have made significant steps in this direction.
Integrable systems, symmetries and representations
The strong and weak as well as electromagnetic interactions – in other words, every force in nature except gravity – are all described by gauge theory. In addition to gauge fields, there are matter fields. The latter represent electrons, neutrinos, quarks and possibly the Higgs boson. Gauge fields mediate forces between particles described by matter fields.

Research within the EU-funded project INTGAUGESTRING (Integrable structures in supersymmetric gauge theory and its string dual) centred on quantum gauge theory in four dimensions. In particular, the maximally supersymmetric Yang-Mills theory, for short N=4 SYM, provided a ‘laboratory’ for studying different aspects of quantum field theory.

Over three years of intensive study of dynamic observables offered valuable insights into planar gauge theory and its dual string theory. Scientists developed a new method for computing three-point correlation functions of local operators in the case of strong coupling. Subsequently, they could derive previously unknown structure constants.

The team formulated amplitude deformations of the Graßmannian integral for scattering amplitudes. In the planar limit, the N=4 SYM theory is conjectured to be integrable. This integrability was well established for the spectral problem of anomalous dimensions. But before INTGAUGESTRING, little was known about integrability for scattering amplitudes.

The study of scattering amplitudes led scientists to the multi-Regge limit of high-energy scattering. Besides its phenomenological importance, it had long been discovered that perturbative expansion is simpler in this limit. First, they isolated Regge cut contributions and then, expanded contributions to a given region to the three- and four-loop order.

INTGAUGESTRING results contribute to understanding the dynamics of interacting gauge theories at a fundamental level. Further efforts are already devoted to obtaining a complete solution of the N=4 SYM theory’s dynamic observables. Although it does not model real-world physics, it shares common features with more realistic theories, including the quantum chromodynamics of strong interactions.

Related information


Standard model of particle physics, gauge theory, INTGAUGESTRING, supersymmetric Yang-Mills theory, string theory
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